Interpret this... (PHPem 2016)
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First half of a two-part talk. I'll show how the Lexer, Parser and AST work in PHP, introducing a little bit of compiler theory that helps explain.
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-9-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-10-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-11-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-12-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-13-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-14-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-15-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-16-320.jpg)
![@asgrim
zend_language_scanner.l
<ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" {
yy_push_state(ST_LOOKING_FOR_VARNAME);
RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES);
}
<ST_LOOKING_FOR_VARNAME>{LABEL}[[}] {
yyless(yyleng - 1);
zend_copy_value(zendlval, yytext, yyleng);
yy_pop_state();
yy_push_state(ST_IN_SCRIPTING);
RETURN_TOKEN(T_STRING_VARNAME);
}](https://image.slidesharecdn.com/161126-interpretthisphpem2016-161126153237/85/Interpret-this-PHPem-2016-17-320.jpg)
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Interpret this... (PHPem 2016)
- 1. @asgrim Interpret this… James Titcumb PHPem Unconference 2016
- 2. Who is this guy? James Titcumb www.jamestitcumb.com www.roave.com www.phphants.co.uk www.phpsouthcoast.co.uk @asgrim
- 3. @asgrim How PHP works PHP code OpCache Execute (VM) Lexer + Parser Compiler
- 5. @asgrim zend_language_scanner.l <ST_IN_SCRIPTING>"exit" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"die" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"function" { RETURN_TOKEN(T_FUNCTION); }
- 6. @asgrim zend_language_scanner.l <ST_IN_SCRIPTING>"exit" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"die" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"function" { RETURN_TOKEN(T_FUNCTION); }
- 7. @asgrim zend_language_scanner.l <ST_IN_SCRIPTING>"exit" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"die" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"function" { RETURN_TOKEN(T_FUNCTION); }
- 8. @asgrim zend_language_scanner.l <ST_IN_SCRIPTING>"exit" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"die" { RETURN_TOKEN(T_EXIT); } <ST_IN_SCRIPTING>"function" { RETURN_TOKEN(T_FUNCTION); }
- 9. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 10. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 11. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 12. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 13. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 14. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 15. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 16. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 17. @asgrim zend_language_scanner.l <ST_DOUBLE_QUOTES,ST_BACKQUOTE,ST_HEREDOC>"${" { yy_push_state(ST_LOOKING_FOR_VARNAME); RETURN_TOKEN(T_DOLLAR_OPEN_CURLY_BRACES); } <ST_LOOKING_FOR_VARNAME>{LABEL}[[}] { yyless(yyleng - 1); zend_copy_value(zendlval, yytext, yyleng); yy_pop_state(); yy_push_state(ST_IN_SCRIPTING); RETURN_TOKEN(T_STRING_VARNAME); }
- 22. @asgrim zend_language_parser.y if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ;
- 23. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 24. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 25. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 26. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 27. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 28. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 29. @asgrim if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ; zend_language_parser.y
- 30. @asgrim if ($a == 1) { a(); } else if ($b == 1) { b(); } else { c(); } Using the rules to parse
- 31. @asgrim if ($a == 1) { a(); } else if ($b == 1) { b(); } else { c(); } Using the rules to parse if_stmt_without_else (A)
- 32. @asgrim if ($a == 1) { a(); } else if ($b == 1) { b(); } else { c(); } Using the rules to parse if_stmt_without_else (A) if_stmt_without_else (B)
- 33. @asgrim if ($a == 1) { a(); } else if ($b == 1) { b(); } else { c(); } Using the rules to parse if_stmt_without_else (A) if_stmt_without_else (B) if_stmt
- 34. @asgrim Zend_language_parser.y (PHP 7.0.10) if_stmt: if_stmt_without_else %prec T_NOELSE { $$ = $1; } | if_stmt_without_else T_ELSE statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, NULL, $3)); } ; if_stmt_without_else: T_IF '(' expr ')' statement { $$ = zend_ast_create_list(1, ZEND_AST_IF, zend_ast_create(ZEND_AST_IF_ELEM, $3, $5)); } | if_stmt_without_else T_ELSEIF '(' expr ')' statement { $$ = zend_ast_list_add($1, zend_ast_create(ZEND_AST_IF_ELEM, $4, $6)); } ;
- 35. @asgrim zend_language_parser.y (PHP 5.6.26) T_IF parenthesis_expr { zend_do_if_cond(&$2, &$1 TSRMLS_CC); } statement { zend_do_if_after_statement(&$1, 1 TSRMLS_CC); } void zend_do_if_cond(const znode *cond, znode *closing_bracket_token TSRMLS_DC) { int if_cond_op_number = get_next_op_number(CG(active_op_array)); zend_op *opline = get_next_op(CG(active_op_array) TSRMLS_CC); opline->opcode = ZEND_JMPZ; SET_NODE(opline->op1, cond); closing_bracket_token->u.op.opline_num = if_cond_op_number; SET_UNUSED(opline->op2); INC_BPC(CG(active_op_array)); }
- 36. @asgrim AST is new in PHP 7+
- 37. @asgrim How PHP works PHP code OpCache Execute (VM) Lexer + Parser Compiler
- 39. @asgrim First… WTF is AST?
- 40. @asgrim AST is just a data structure
- 41. @asgrim PHP code <?php echo "Hello world";
- 42. @asgrim An AST representation Echo statement `-- String, value "Hello world"
- 43. @asgrim PHP code <?php echo "Hello " . "world";
- 44. @asgrim An AST representation Echo statement `-- Concat |-- Left | `-- String, value "Hello " `-- Right `-- String, value "world"
- 45. @asgrim PHP code <?php $a = 5; $b = 3; echo $a + ($b * 2);
- 46. @asgrim An AST representation Assign statement |-- Variable $a `-- Integer, value 5 Assign statement |-- Variable $b `-- Integer, value 3 Echo statement `-- Add operation |-- Left | `-- Variable $a `-- Right `-- Multiply operation |-- Left | `-- Variable $b `-- Right `-- Integer, value 2
- 47. @asgrim AST compilation Statements EchoAssign Scalar value: (int)5 Variable name: $a Assign Scalar value: (int)3 Variable name: $b Add op Right operandLeft operand Variable name: $a Multiply op Right operandLeft operand Variable name: $b Scalar value: (int)2
- 48. @asgrim AST compilation: pre-order traversal Statements EchoAssign Scalar value: (int)5 Variable name: $a Assign Scalar value: (int)3 Variable name: $b Add op Right operandLeft operand Variable name: $a Multiply op Right operandLeft operand Variable name: $b Scalar value: (int)2
- 49. @asgrim Pre-order traversal: Polish notation Assign(Variable $a, Scalar 5) Assign(Variable $b, Scalar 3) Echo ( Add( Variable $a, Multiply( $b, 2 ) ) )
- 50. @asgrim Order of precedence 1 + 2 * 3 = 1 + (2 * 3) = 7? = (1 + 2) * 3 = 9?
- 51. @asgrim Order of precedence 1 + 2 * 3 = 1 + (2 * 3) = 7? = (1 + 2) * 3 = 9? + 1 * 2 3
- 52. @asgrim Order of precedence 1 + 2 * 3 = 1 + (2 * 3) = 7? = (1 + 2) * 3 = 9? + 1 * 2 3 Operator Left operand Right operand
- 53. @asgrim Order of precedence 1 + 2 * 3 = 1 + (2 * 3) = 7? = (1 + 2) * 3 = 9? + 1 * 2 3 Operator Left operand Right operand Operator Left operand Right operand
- 54. @asgrim Reverse Polish Notation 1 2 3 * +
- 55. @asgrim Reverse Polish Notation 1 2 3 * + The stack
- 56. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1
- 57. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1 2
- 58. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1 2 3
- 59. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1 2 3
- 60. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1 2 3
- 61. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1 6
- 62. @asgrim Reverse Polish Notation 1 2 3 * + The stack 1 6
- 63. @asgrim Reverse Polish Notation 1 2 3 * + The stack 7
- 64. Any questions? James Titcumb @asgrim